(CNN) -- Heavy rains tied to the Atlantic hurricane season's first named storm contributed to three deaths and led to the evacuation of thousands of people in Mexico, the state-run news agency reported.
Tropical Storm Arlene had lost most of its wind-strength by Friday, as it passed over the Latin American nation. In an advisory issued late Thursday, the U.S. National Weather Service noted that the storm was dissipating over the Sierra Madre Mountains in Mexico and noted that all coastal warnings had since expired.
Yet even after its sustained winds decreased to 40 mph or less, Arlene continued to wreak havoc -- especially in hard-hit areas prone to mudslides and flash floods.
Besides the deaths and evacuations, official news agency Notimex reported that the storm had destroyed power lines and hundreds of buildings, many of them residences. Officials are warning residents not to leave their homes, given the difficult conditions.
Authorities declared a "state of emergency" in the state of Hidalgo, in eastern Mexico, reported Notimex. Heavily polluted canals in Valle de Chaco and other areas in and around Mexico City have overflowed, spurring concerns about water-borne illnesses.
Mexico's national weather service said that the coastal areas of Costa Grande, in the state of Guerrero, should see significant rainfall through Sunday.
The Atlantic hurricane season spans June 1 to November 30.